Question 994514
Assign some variables.
{{{system(r=unknownPlaneSpeed,w=40WindSpeed,m=410MilesWithWind,n=310MilesAgainstWind,t=unknownSameTimeBothDirections)}}}


Uniform Rates Travel Rule, RT=D to relate rate, time, distance;
also can be used as R=D/T.

<pre>
Direction   speed        time       distance
WITH        r+w           t          m
AGAINST     r-w           t          n
</pre>
See that the same number in the same variable t is used for both directions.  The question asks for r, but not for t.
<pre>
Direction   speed        time              distance
WITH        r+w           t=m/(r+w)          m
AGAINST     r-w           t=n/(r-w)          n
</pre>


Equate the two formulas for time t:
{{{highlight(m/(r+w)=n/(r-w))}}}
This equation uses only one unknown variable, r, which is what the question asks to find.  Solve the equation for r.